We introduce nil 3-Armendariz rings, which are generalization of 3-Armendariz rings and nil Armendaiz rings and investigate their properties. We show that a ring R is nil 3-Armendariz ring if and only if for any , Tn(R) is nil 3-Armendariz ring. Also we prove that a right Ore ring R is nil 3-Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result, we can show that a commutative ring R is nil 3-Armendariz if and only if the total quotient ring of R is nil 3-Armendariz.
Cite this paper
E. Ali, A. Elshokry and Z. Liu, "Nil 3-Armendariz Rings," Advances in Pure Mathematics
, Vol. 3 No. 9, 2013, pp. 703-708. doi: 10.4236/apm.2013.39096
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